Mathematical averaging apparatus



April 8, 1969 R. s. WHITE MATHEMATICAL AVERAGING APPARATUS Filed June26, 1967 INVENTOR. ROY S. WHITE IHlSm United States Patent O 3,437,268MATHEMATICAL AVERAGING APPARATUS Roy S. White, Rte. 1, Cleveland, N.C.27013 Filed June 26, 1967, Ser. No. 648,887 Int. ci. Guam 1/12 U.S. Cl.235-61 8 Claims ABSTRACT F THE DISCLOSURE This invention relates todevices for performing mathematical operations and more particularly toan apparatus utilizing volume-ratio principles by which the average ofseveral numbers may be quickly obtained through varying the volume ofone container proportionally by the use of one or more volume segmentswith respect to the constant volume of a second container.

Background, brief summary and objectives of the invention Numerousclerical and teaching tasks require repetitive averaging of a `quantityof numbers to obtain information useful in daily business and schoolactivities. IFor example, in the course of the school year, a highschool teacher must add approximately twelve thousand quantities andperform some two thousand seven hundred divisions in averaging grades ofstudents. This obviously demands a great deal of time for monitoringstudent progress which time could be more productively spent in directinstructional periods. While a number of devices are available forobtaining grade averages such as that disclosed in U.S. Patent No.1,023,961, none of the devices known utilizes a hydraulic circuit inaccomplishing the averaging operation. Most of the devices are comprisedof a number of graduated scales positioned in a side-by-siderelationship so that an average number may be read directly orinterpolated from a number of input quantities.

The division step which must be performed in obtaining the average valueof a group of quantities is accomplished in the present invention as theresult of the speciiic dimensional ratios between cross-sectional areasof an accumulator tube, a force-tube and a number of volume segmentswhich can be inserted in the accumulating tube to make volumeadjustments. The cross-sectional area of one volume segment is equal tothe internal cross-sectional area of the force-tube, and the internalcross-sectional area of the accumulator tube is equal in the preferredembodiment to ten times the internal cross-sectional area of theforce-tube. Thus the volume segments are used to reduce the effectiveinternal cross-sectional area of the accumulator tube, and the additionof one such segment produces a ratio of 9:1 between the elfecti'veinternal cross-sectional area of the accumulator tube and the internalcross-sectional area of the force-tube. The positioning of additionalvolume segments 'within the accumulator tube changes the ratio to 8:1when adding two volume segments, 7:1 when adding three segments; 6:1when adding four, and so on.

The addition operation which is initially required in obtaining theaverage value of a group of quantities is accomplished by introducingvolumes of fluid corresponding to the individual quantities in the groupto be averaged into the accumulator tube. Thus where X1, X2,

3,437,268 Patented Apr. 8, 1969 X3 Xn are quantities in a group of nquantities for which the average is to be found, the equation governingthe equation being valid provided in the embodiment shown that X isequal to or greater than 50.

With the foregoing in mind, it is therefore an object of the presentinvention to provide an apparatus for performing averaging computationsutilizing a hydraulic circuit in accomplishing this operation.

Another object of the present invention is to provide a practicalmachine for use by school teachers and instructors in averaging gradesand the like.

A further object of the present invention is to provide an apparatus ofthe type described which may be made of a size and capacity sucient toverify a known mathematical formula for an infinite number of quantitiesto be averaged.

Yet still another object of the present invention is to provide anapparatus of the type described which has a minimum of moving mechanicalparts and is thus simple in construction, reliable in operation andeconomical to manufacture.

Many of the other objects and attendant advantages of the presentinvention will become more obvious from the following detaileddescription ta-ken in conjunction with the drawings in which likecharacters of reference designate like parts.

Figure description lFIG. l is a perspective view of the preferredembodiment of the present invention showing the force-tube andadjacently positioned accumulator tube, both tubes aligned with respectto a graduated scale placed therebetween.

FIG. 2 is a plan view of the preferred embodiment of the averagingapparatus shown in FIG. 1 illustrating the placement of eight volumesegments within the accumulator tube to adjust the volumecross-sectional area ratio between the accumulator tube and theforce-tube.

FIG. 3 is a perspective View of a single volume segment, one or more ofwhich are used to adjust the volume ration of the accumulator tube withrespect to the force-tube consistent with the number of quantities to beaveraged.

FIG. 4 is a side elevational sectional view of a preferred embodiment ofa grade averaging apparatus as illustrated in FIG. 1 showing thehydraulic connections between the force-tube and the accumulator tubeand the air relief valving in the force-tube plunger.

Detailed description of the invention Referring now to the drawings andparticularly to FIG. 4, a reservoir |10 designed to accommodate a supplyof lluid is encapsulated by a generally cylindrical body portion 12closed at the top and bottom by appropriately designed caps 14 and 16,the top cap 14 containing an air vent 17 to provide free fluid ow withinthe reservoir and related components by pressure equalization. Anaccumulator tube generally designated 18 is positioned on the top cap 14and communicates with the reservoir 10` by means of an orice 20 havingan extended lip 22 extending into the accumulator tube chamber 24. Aplunger 26 extends longitudinally within chamber 24 of accumulator tube18 and is elevated to some degree above the top 28 of the accumulatortube for manual manipulation. The plunger has a stopper portion 30which, when positioned within lip 22, seals orifice 20I to prevent thefiow of fluid from within the accumulator tube chamber 24 back toreservoir 10` unless the plunger 26 is removed.

A second orifice 32 provides a connection from the chamber 24 ofaccumulator tube 18 to the accumulator tube check valve shell generallydesignated 34. Check valve shell 34 includes a ball valve seat 36containing a third orifice 38, the orifice being controlled by a ballvalve 40 normally seated therein.

A ver-tical force-tube shown generally as 42 is integral with andextends upwardly through top cap 14 from reservoir 10, the tube having alower portion 44 extending substantially within the reservoir. The tubelower portion 44 has a ball seat 46 containing another orifice 48 whichallows fluid communication between the forcetube 42 and the reservoir. Aball valve 50` controls the opening of this orifice by operating assubsequently described.

The lower portion 44 of force-tube 42 is connected to the check valveshell 34 by a passageway 52 which will permit fluid flow therethroughduring the averaging operation also to be described subsequently.

A hollow plunger 54 telescopes within force-tube 42 in a snuglylslidable manner so that fiuid flow may be induced into or from the tubeduring the averaging operation. Additionally, an indicator 56 is securedto and extends from plunger 54 downwardly so as to directly indicatereadings of quantities to be averaged. Plunger 54 has a bore S extendingthroughout its length but which is restricted in size at the lowerportion 57 to form a ball seat 61 having another orifice 63. A ballvalve 65 and shiftable weight S11 control the opening by operating in amanner to be subsequently described.

A connecting web 58 spans the force-tube 42 and the accumulator tube 18and holds a graduated scale placed thereon for use by the operator inaveraging a given number of quantities on the present invention.

The operation of the present invention is initiated by filling thereservoir with a liquid preferably containing some coloring ingredientto make it readily visible when positioned within the accumulator tubeand the forcetube. Plunger 54 is then depressed to its lowest positionand then raised to some intermediate position. When the plunger israised, atmospheric pressure forces the liquid to raise the ball valve50 from its seat 46 and enter the space formerly occupied by the plunger54. As there is usually an air pocket between the liquid and the plunger54, this pocket must be removed before the device can be operated withaccuracy. Removal is accomplished by placing the top 55 of the otherplunger 26 against ball so as to retain that ball on its seat 36, andthen urging plunger `54 downwardly. The pressure of the trapped airbetween the plunger 54 and the liquid in the force-tube 42 causes theball 65 and the movable weight 51 positioned atop the ball to rise fromits seat 61 within the bore 55 of plunger 54, and the trapped air thenescapes through the top 59 of the bore 5S of force-tube 42. The weight51, which has a diameter sufficiently small to allow air passage alongits sides within bore 55 of tube 42 retains the ball valve 65 on seat 61during subsequent opera-tions.

After releasing the ball valve 40 and replacing plunger 26 in orifice20, the plunger 54 is depressed, the ball valve remains over orifice 48and the liquid is forced through the connecting passageway or cross-overtube 52 to the accumulator tube check valve shell 34 where it raisesball valve 40 from orifice 38 and enters the accumulator tube 18 throughorifice 32. The fuid remains in the accumulator tube until the sealer 30is withdrawn from opening 20 which then allows the fiuid in theaccumulator to return to the reservoir 10.

The divisional operation which must be performed in finding the averagevalue of a group of quantities is accomplished because of the specificdimensional ratios between the cross-sectional areas of the accumulatortube 18 and the force-tube 42 and the volume segments, one of which isshown in FIG. 3 and designated 60. The crosssectional area of a volumesegment `60 is equal to the internal cross-sectional area of theforce-tube 42, and the internal cross-sectional area of the accumulatortube 118 is equal, in the preferred embodiment shown, to ten times theinternal cross-sectional area of the force-tube 42. The volume segments60 are used to reduce the effective internal cross-sectional area of theaccumulator tube, and that addition of one such segment to theaccumulator tube produces a ratio of 9:1 between the effective internalcross-sectional area of the accumulator tube and the internalcross-sectional area of the force-tube. The addition of subsequentsegments to the accumulator tube produces a diminishing ratio of 8:1 iftwo segments are added, 7:1 if three segments are added, 6:1 if foursegments are added, and so on. In averaging a group of ten quantities,no volume segments are used, but when less than ten quantities are to beaveraged, the number of volume segments to be used can be determined byuse of the formula S=lO-N, where S is the number of volume segments tobe used and N is the number of quantities in the group to be averaged.

The operation of addition, which also must be performed in finding theaverage value of a group of quantities, is accomplished by causingquantities of liquid which represent the values of each of the originalquantities in the group to be averaged to accumulate inthe accumulatortube. The quotients `are produced by the action of the ratio between theeffective internal areas of the accumulator tube and the force-tube asexplained above.

The average value of a group of numerical quantities is found by fillingthe reservoir with liquid and the correct number of volume segmentsdetermined by the number of quantities to abe averaged. The plunger 54is then depressed to its lowest position and subsequently raised toydraw in liquid until the sealing ring 62 (in the event an indicator 56is not used) registers with the quantity mark on the graduated scale 58representing one of the group numbers to be averaged. The plunger isthen depressed until the sealing ring 62 aligns with the 50 mark on thegraduated scale. The plunger 54 is then again raised until the ringregisters with the graduated scale mark which indicates the value of thesecond quantity in the group after which it is again depressed until thesealing ring registers with the lowest graduated mark on the sca-le or,as indicated above in this embodiment, the 50 graduation scale. Theprocedure is then repeated for each quantity in the group of quantitiesto be averaged. The liquid level in the accumulator tube then indicatesthe average on the graduated scale 58.

As is `apparent from the above description, it is possible to find theaverage of n quantities while using the present invention by raising anddepressing the plunger 54 n times after which the computed average maybe read from the graduated scale line which coincides with the liquidlevel in the accumulator tube 18. The capacity of a grade averaging4device such as is disclosed herein can be varied by providing theaccumulator tube and force-tube with larger or smaller diameters andconstructing volume segments of larger or smaller graduations ifnecessary. Since the manual addition and subsequent manual divisionrequired in averaging a given number of quantities is eliminated, andsince little mental activity is required t0 operate the embodiment ofthe invention herein set forth, teachers, instructors `and the like canaverage grades or numbers in approximately one-quarter of the timerequired for manual averaging with considerably less mental fatigue.

Obviously, many modifications and variations may be made in theconstruction and arrangement of the accumulator tube, the force-tube,the graduated scale, and the interconnecting hydraulic passageconnecting the two, as Well as the other phases of the present inventiveconcept in light of the above teachings without departing from the realspirit and purpose of this invention. Such modifications of parts aswell as the use of equivalents to those herein illustrated and describedare reasonably included and contemplated.

I claim:

1. A device for computing the average value of Ia number of quantitiescomprising: a fluid supply; first fluid container means; second fluidcontainer means operatively connected to said first means; means formeasuring the fluid quantity in said iirst and second container means;means for inducing fluid representing a quantity to be averaged intosaid first container means and from said first container means into saidsecond container means; and means for varying the volume of said seconduid container means according to a predetermined relationship where- Ibya number of quantities represented by fluid volume may be averaged andthe average value of the quantities indicated by the measuring meansaccording to the fiuid contained in the second fluid container means.

2. A device as claimed in claim 1 further comprising: a reservoir forretaining said fluid supply operatively c011- nected with said first andsecond iluid container means.

3. A device as claimed in claim 1, said measuring means including agraduated scale positioned to indicate uid level in said rst and secondcontainer means.

4. A ,device as claimed in claim 2, said inducing means including apiston mounted in said first container means operable to draW a Huidquantity from said reservoir into said first container means and forcethe fluid quantity into said second container means.

5. A device as claimed in claim 2, said varying means including insertmeans for varying the effective volume of said second container means.

6. A device as claimed in claim 2, said iirst iluid container meansincluding a vertical force-tube.

7. A device as claimed in claim 2, said second Huid container meansincluding a vertical accumulator tube.

S. A device as claimed in claim 2, said measuring means including agraduated scale positioned to indicate Huid level in said first andsecond container means, said inducing means including a piston mountedin said rst container means operable to draw a uid quantity from saidreservoir into said first container means and force the uid quantityinto said second container means, said varying means including insertmeans for varying the effective volume of said second container means,said first fluid container means including a vertical force-tube, andsaid second fiuid container means including a vertical accumulator tube.

References Cited UNITED STATES PATENTS 3,217,545 11/ 1965 Kreisman73-400 RICHARD B. WILKINSON, Primary Examiner. L. R. FRANKLIN, AssistantExaminer.

U.S. Cl. X.R. 23S- 200

